The source of the data is here: https://archive.ics.uci.edu/ml/datasets/Wine+Quality
Original citation: P. Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis. Modeling wine preferences by data mining from physicochemical properties. In Decision Support Systems, Elsevier, 47(4):547-553, 2009.
This data consists of two datasets. Each dataset contains quality ratings for wines as well as 11 features of these wines. The 12 variables are all continuous and numeric. The first dataset contains 1599 observations of red wines; the second dataset contains 4898 observations of white wines.
df <- as_tibble(read.table("winequality-red.csv", sep=";", header = TRUE))
summary(df$quality)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.636 6.000 8.000
df_white <- as_tibble(read.table("winequality-white.csv", sep=";", header = TRUE))
summary(df_white$quality)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.878 6.000 9.000
The variables in the data all have different scales. For example:
summary(df$fixed.acidity)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.60 7.10 7.90 8.32 9.20 15.90
summary(df_white$sulphates)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.2200 0.4100 0.4700 0.4898 0.5500 1.0800
The data will be standardized to make some plots of the data easier to visualize.
data_red <- as.data.frame(scale(df))
summary(data_red$fixed.acidity)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.1364 -0.7005 -0.2410 0.0000 0.5056 4.3538
data_white <- as.data.frame(scale(df_white))
summary(data_white$sulphates)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.3645 -0.6996 -0.1739 0.0000 0.5271 5.1711
Glancing at the raw data, we see that the red wine quality ratings are not distributed uniformly, and there are a few outlier ratings. Our model will probably not perform well when predicting red wine ratings below 4 or above 7.
hist(df$quality,
main="Histogram of Red Wine Quality Ratings",
xlab="Rating",
las=1,
breaks=4)
The white wine ratings are distributed similarly, although a bit more symmetrically. Our model will probably not perform well when predicting white wine ratings below 4 or above 8.
hist(df_white$quality,
main="Histogram of White Wine Quality Ratings",
xlab="Rating",
las=1,
breaks=5)
We may consider winsorizing or truncating our dataset to only consider observations where the rating was above 4 and below 7 (or 8, for white wine).
Looking at the standardized data, there are a few variables that immediately appear to be predictive of the quality. Alcohol is one:
ggplot(data_red, aes(x=alcohol, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Alcohol Content vs. Quality Rating",
subtitle="Red Wine",
y="Quality",
x="Alcohol")
Volatile acidity is another one:
ggplot(data_red, aes(x=volatile.acidity, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Volatile Acidity vs. Quality Rating",
subtitle="Red Wine",
y="Quality",
x="Acidity")
These variables will likely be useful for predicting quality ratings of white wine as well:
ggplot(data_white, aes(x=alcohol, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Alcohol Content vs. Quality Rating",
subtitle="White Wine",
y="Quality",
x="Alcohol")
ggplot(data_white, aes(x=volatile.acidity, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Volatile Acidity vs. Quality Rating",
subtitle="White Wine",
y="Quality",
x="Acidity")
The data will be split into train and test datasets. The model will be trained on the train data and evaluated on the test data.
index = sample(1:nrow(df), 0.7*nrow(df))
train = df[index,] # Create the training data
test = df[-index,] # Create the test data
dim(train)
## [1] 1119 12
dim(test)
## [1] 480 12
lm_basic <- lm(data = df, quality ~ .)
summary(lm_basic)
##
## Call:
## lm(formula = quality ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.68911 -0.36652 -0.04699 0.45202 2.02498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.197e+01 2.119e+01 1.036 0.3002
## fixed.acidity 2.499e-02 2.595e-02 0.963 0.3357
## volatile.acidity -1.084e+00 1.211e-01 -8.948 < 2e-16 ***
## citric.acid -1.826e-01 1.472e-01 -1.240 0.2150
## residual.sugar 1.633e-02 1.500e-02 1.089 0.2765
## chlorides -1.874e+00 4.193e-01 -4.470 8.37e-06 ***
## free.sulfur.dioxide 4.361e-03 2.171e-03 2.009 0.0447 *
## total.sulfur.dioxide -3.265e-03 7.287e-04 -4.480 8.00e-06 ***
## density -1.788e+01 2.163e+01 -0.827 0.4086
## pH -4.137e-01 1.916e-01 -2.159 0.0310 *
## sulphates 9.163e-01 1.143e-01 8.014 2.13e-15 ***
## alcohol 2.762e-01 2.648e-02 10.429 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared: 0.3606, Adjusted R-squared: 0.3561
## F-statistic: 81.35 on 11 and 1587 DF, p-value: < 2.2e-16
Volatile acidity, chlorides, total sulfur dioxide, sulphates and alcohol are all very statistically significant, although our adjusted \(R^2\) is still quite low.
train_control <- trainControl(method = "cv", number = 5)
model_ridge <- train(quality ~ .,
data = df,
method = "ridge", # method
trControl = train_control) # cross validation
model_ridge
## Ridge Regression
##
## 1599 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 1278, 1281, 1280, 1279, 1278
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0e+00 0.6518467 0.3531630 0.5045061
## 1e-04 0.6518452 0.3531658 0.5045037
## 1e-01 0.6517271 0.3537885 0.5035855
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.1.
#something doesn't seem to be working here
model_stepwise <- train(quality ~ .,
data = df,
method = "glmStepAIC",
trControl = train_control)
## Start: AIC=2604.74
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 562.43 2602.9
## - fixed.acidity 1 562.53 2603.1
## - residual.sugar 1 562.60 2603.2
## - citric.acid 1 562.63 2603.3
## <none> 562.38 2604.7
## - free.sulfur.dioxide 1 563.65 2605.6
## - pH 1 564.05 2606.6
## - chlorides 1 568.31 2616.2
## - total.sulfur.dioxide 1 570.81 2621.8
## - sulphates 1 580.96 2644.3
## - volatile.acidity 1 589.37 2662.7
## - alcohol 1 598.81 2683.0
##
## Step: AIC=2602.86
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 562.54 2601.1
## - residual.sugar 1 562.60 2601.2
## - citric.acid 1 562.69 2601.4
## <none> 562.43 2602.9
## - free.sulfur.dioxide 1 563.74 2603.8
## - pH 1 565.40 2607.6
## - chlorides 1 568.48 2614.5
## - total.sulfur.dioxide 1 571.02 2620.3
## - sulphates 1 581.83 2644.2
## - volatile.acidity 1 590.21 2662.5
## - alcohol 1 651.33 2788.6
##
## Step: AIC=2601.11
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 562.69 2599.5
## - residual.sugar 1 562.73 2599.6
## <none> 562.54 2601.1
## - free.sulfur.dioxide 1 563.90 2602.2
## - pH 1 567.58 2610.5
## - chlorides 1 569.55 2614.9
## - total.sulfur.dioxide 1 572.35 2621.2
## - sulphates 1 582.25 2643.2
## - volatile.acidity 1 591.11 2662.5
## - alcohol 1 652.30 2788.4
##
## Step: AIC=2599.46
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 562.85 2597.8
## <none> 562.69 2599.5
## - free.sulfur.dioxide 1 564.22 2600.9
## - pH 1 568.16 2609.8
## - chlorides 1 570.27 2614.6
## - total.sulfur.dioxide 1 573.13 2621.0
## - sulphates 1 582.25 2641.2
## - volatile.acidity 1 597.57 2674.4
## - alcohol 1 654.33 2790.4
##
## Step: AIC=2597.81
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 562.85 2597.8
## - free.sulfur.dioxide 1 564.52 2599.6
## - pH 1 568.58 2608.8
## - chlorides 1 570.32 2612.7
## - total.sulfur.dioxide 1 573.15 2619.0
## - sulphates 1 582.28 2639.2
## - volatile.acidity 1 597.72 2672.7
## - alcohol 1 656.21 2792.1
## Start: AIC=2545.03
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - pH 1 537.31 2543.4
## - residual.sugar 1 537.59 2544.1
## - density 1 537.95 2545.0
## <none> 537.14 2545.0
## - citric.acid 1 538.51 2546.3
## - fixed.acidity 1 538.66 2546.7
## - free.sulfur.dioxide 1 538.69 2546.7
## - total.sulfur.dioxide 1 542.46 2555.7
## - chlorides 1 543.32 2557.7
## - sulphates 1 562.78 2602.6
## - volatile.acidity 1 567.79 2614.0
## - alcohol 1 568.31 2615.1
##
## Step: AIC=2543.45
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 538.04 2543.2
## <none> 537.31 2543.4
## - citric.acid 1 538.64 2544.6
## - free.sulfur.dioxide 1 538.76 2544.9
## - density 1 539.28 2546.1
## - fixed.acidity 1 542.16 2552.9
## - total.sulfur.dioxide 1 542.47 2553.7
## - chlorides 1 543.36 2555.8
## - sulphates 1 563.81 2603.0
## - volatile.acidity 1 567.96 2612.4
## - alcohol 1 576.41 2631.2
##
## Step: AIC=2543.19
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + density + sulphates +
## alcohol
##
## Df Deviance AIC
## <none> 538.04 2543.2
## - citric.acid 1 539.30 2544.2
## - density 1 539.30 2544.2
## - free.sulfur.dioxide 1 539.66 2545.0
## - fixed.acidity 1 542.24 2551.1
## - total.sulfur.dioxide 1 542.82 2552.5
## - chlorides 1 543.77 2554.7
## - sulphates 1 563.81 2601.0
## - volatile.acidity 1 569.04 2612.8
## - alcohol 1 591.05 2661.3
## Start: AIC=2516.37
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 525.27 2514.5
## - density 1 525.34 2514.7
## - citric.acid 1 525.53 2515.1
## <none> 525.22 2516.4
## - residual.sugar 1 526.15 2516.6
## - free.sulfur.dioxide 1 526.40 2517.2
## - pH 1 527.79 2520.6
## - total.sulfur.dioxide 1 531.15 2528.7
## - chlorides 1 532.48 2531.9
## - volatile.acidity 1 549.64 2572.4
## - sulphates 1 553.38 2581.1
## - alcohol 1 560.96 2598.5
##
## Step: AIC=2514.48
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 525.35 2512.7
## - citric.acid 1 525.53 2513.1
## <none> 525.27 2514.5
## - residual.sugar 1 526.20 2514.8
## - free.sulfur.dioxide 1 526.51 2515.5
## - pH 1 531.69 2528.0
## - total.sulfur.dioxide 1 531.76 2528.2
## - chlorides 1 533.08 2531.3
## - volatile.acidity 1 549.64 2570.4
## - sulphates 1 553.73 2579.9
## - alcohol 1 579.06 2637.1
##
## Step: AIC=2512.68
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 525.88 2512.0
## <none> 525.35 2512.7
## - residual.sugar 1 526.24 2512.8
## - free.sulfur.dioxide 1 526.61 2513.7
## - total.sulfur.dioxide 1 531.79 2526.2
## - pH 1 531.82 2526.3
## - chlorides 1 533.08 2529.3
## - volatile.acidity 1 552.29 2574.6
## - sulphates 1 554.58 2579.9
## - alcohol 1 620.67 2723.8
##
## Step: AIC=2511.98
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 526.61 2511.7
## <none> 525.88 2512.0
## - free.sulfur.dioxide 1 527.44 2513.8
## - pH 1 532.11 2525.0
## - total.sulfur.dioxide 1 533.09 2527.4
## - chlorides 1 534.31 2530.3
## - sulphates 1 554.73 2578.2
## - volatile.acidity 1 556.80 2583.0
## - alcohol 1 621.73 2723.9
##
## Step: AIC=2511.74
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 526.61 2511.7
## - free.sulfur.dioxide 1 528.37 2514.0
## - pH 1 533.34 2526.0
## - total.sulfur.dioxide 1 533.43 2526.2
## - chlorides 1 534.77 2529.4
## - sulphates 1 555.14 2577.2
## - volatile.acidity 1 557.27 2582.1
## - alcohol 1 625.95 2730.6
## Start: AIC=2501.18
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - free.sulfur.dioxide 1 518.73 2500.3
## <none> 518.26 2501.2
## - density 1 519.08 2501.2
## - fixed.acidity 1 519.58 2502.4
## - pH 1 519.70 2502.7
## - citric.acid 1 519.88 2503.2
## - residual.sugar 1 519.96 2503.4
## - total.sulfur.dioxide 1 524.08 2513.5
## - chlorides 1 524.27 2513.9
## - sulphates 1 535.27 2540.5
## - volatile.acidity 1 543.90 2561.0
## - alcohol 1 556.66 2590.7
##
## Step: AIC=2500.35
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + density + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## <none> 518.73 2500.3
## - density 1 519.68 2500.7
## - pH 1 519.97 2501.4
## - fixed.acidity 1 520.28 2502.2
## - residual.sugar 1 520.70 2503.2
## - citric.acid 1 520.76 2503.3
## - chlorides 1 524.54 2512.6
## - total.sulfur.dioxide 1 525.59 2515.2
## - sulphates 1 536.20 2540.8
## - volatile.acidity 1 546.42 2564.9
## - alcohol 1 556.92 2589.3
## Start: AIC=2494.61
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 515.23 2492.6
## - citric.acid 1 515.24 2492.6
## - fixed.acidity 1 515.26 2492.7
## - residual.sugar 1 515.32 2492.8
## <none> 515.23 2494.6
## - free.sulfur.dioxide 1 517.98 2499.4
## - pH 1 518.33 2500.3
## - chlorides 1 523.16 2512.2
## - total.sulfur.dioxide 1 523.75 2513.6
## - sulphates 1 534.90 2540.6
## - volatile.acidity 1 541.22 2555.7
## - alcohol 1 556.50 2591.3
##
## Step: AIC=2492.61
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 515.24 2490.6
## - fixed.acidity 1 515.32 2490.8
## - residual.sugar 1 515.38 2491.0
## <none> 515.23 2492.6
## - free.sulfur.dioxide 1 518.00 2497.5
## - pH 1 519.81 2501.9
## - chlorides 1 523.25 2510.4
## - total.sulfur.dioxide 1 523.80 2511.7
## - sulphates 1 536.10 2541.5
## - volatile.acidity 1 541.44 2554.2
## - alcohol 1 612.72 2712.6
##
## Step: AIC=2490.63
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 515.39 2489.0
## - fixed.acidity 1 515.42 2489.1
## <none> 515.24 2490.6
## - free.sulfur.dioxide 1 518.14 2495.8
## - pH 1 519.82 2500.0
## - chlorides 1 524.12 2510.5
## - total.sulfur.dioxide 1 524.55 2511.6
## - sulphates 1 536.10 2539.5
## - volatile.acidity 1 552.20 2577.4
## - alcohol 1 616.02 2717.5
##
## Step: AIC=2489.01
## .outcome ~ fixed.acidity + volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 515.62 2487.6
## <none> 515.39 2489.0
## - free.sulfur.dioxide 1 518.23 2494.0
## - pH 1 519.98 2498.4
## - chlorides 1 524.45 2509.3
## - total.sulfur.dioxide 1 525.24 2511.3
## - sulphates 1 536.70 2538.9
## - volatile.acidity 1 552.47 2576.0
## - alcohol 1 616.58 2716.6
##
## Step: AIC=2487.57
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 515.62 2487.6
## - free.sulfur.dioxide 1 518.46 2492.6
## - pH 1 521.57 2500.3
## - chlorides 1 524.45 2507.3
## - total.sulfur.dioxide 1 525.24 2509.3
## - sulphates 1 536.71 2536.9
## - volatile.acidity 1 552.49 2574.1
## - alcohol 1 616.65 2714.8
## Start: AIC=3164.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 666.70 3163.0
## - fixed.acidity 1 666.80 3163.2
## - residual.sugar 1 666.91 3163.5
## - citric.acid 1 667.06 3163.8
## <none> 666.41 3164.3
## - free.sulfur.dioxide 1 668.10 3166.3
## - pH 1 668.37 3167.0
## - chlorides 1 674.80 3182.3
## - total.sulfur.dioxide 1 674.84 3182.4
## - sulphates 1 693.38 3225.7
## - volatile.acidity 1 700.03 3241.0
## - alcohol 1 712.08 3268.3
##
## Step: AIC=3162.96
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 666.81 3161.2
## - residual.sugar 1 666.93 3161.5
## - citric.acid 1 667.35 3162.5
## <none> 666.70 3163.0
## - free.sulfur.dioxide 1 668.53 3165.3
## - pH 1 671.02 3171.3
## - total.sulfur.dioxide 1 675.43 3181.8
## - chlorides 1 675.46 3181.8
## - sulphates 1 693.98 3225.1
## - volatile.acidity 1 701.70 3242.8
## - alcohol 1 786.37 3424.9
##
## Step: AIC=3161.22
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 667.06 3159.8
## - citric.acid 1 667.37 3160.6
## <none> 666.81 3161.2
## - free.sulfur.dioxide 1 668.71 3163.8
## - pH 1 673.87 3176.1
## - chlorides 1 676.75 3182.9
## - total.sulfur.dioxide 1 676.84 3183.1
## - sulphates 1 694.48 3224.2
## - volatile.acidity 1 703.04 3243.8
## - alcohol 1 787.44 3425.1
##
## Step: AIC=3159.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 667.54 3159.0
## <none> 667.06 3159.8
## - free.sulfur.dioxide 1 669.13 3162.8
## - pH 1 674.20 3174.9
## - total.sulfur.dioxide 1 676.89 3181.2
## - chlorides 1 676.89 3181.2
## - sulphates 1 694.51 3222.3
## - volatile.acidity 1 703.04 3241.8
## - alcohol 1 789.73 3427.8
##
## Step: AIC=3158.98
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 667.54 3159.0
## - free.sulfur.dioxide 1 669.93 3162.7
## - pH 1 674.61 3173.8
## - total.sulfur.dioxide 1 678.32 3182.6
## - chlorides 1 678.35 3182.7
## - sulphates 1 694.60 3220.5
## - volatile.acidity 1 709.85 3255.3
## - alcohol 1 792.02 3430.4
#model_stepwise
findCorrelation(
cor(df),
cutoff = 0.5,
verbose = TRUE,
names = TRUE
)
## Compare row 3 and column 1 with corr 0.672
## Means: 0.293 vs 0.19 so flagging column 3
## Compare row 1 and column 8 with corr 0.668
## Means: 0.245 vs 0.172 so flagging column 1
## Compare row 7 and column 6 with corr 0.668
## Means: 0.174 vs 0.169 so flagging column 7
## All correlations <= 0.5
## [1] "citric.acid" "fixed.acidity" "total.sulfur.dioxide"
ggcorrplot(correlation_df, hc.order = TRUE, type = "lower")
df_less_acid <- df %>%
select(-citric.acid, -fixed.acidity)
lm_less_acid <- lm(data = df_less_acid, quality ~ .)
summary(lm_less_acid)
##
## Call:
## lm(formula = quality ~ ., data = df_less_acid)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.66740 -0.37223 -0.04556 0.46264 2.03092
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.0575013 12.0089257 1.004 0.3155
## volatile.acidity -1.0127925 0.1009279 -10.035 < 2e-16 ***
## residual.sugar 0.0115046 0.0134606 0.855 0.3929
## chlorides -2.0490938 0.3992190 -5.133 3.21e-07 ***
## free.sulfur.dioxide 0.0048741 0.0021385 2.279 0.0228 *
## total.sulfur.dioxide -0.0035687 0.0006939 -5.143 3.03e-07 ***
## density -7.5668358 11.8648390 -0.638 0.5237
## pH -0.4919908 0.1210931 -4.063 5.08e-05 ***
## sulphates 0.9024434 0.1129657 7.989 2.60e-15 ***
## alcohol 0.2810022 0.0201992 13.912 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1589 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3562
## F-statistic: 99.22 on 9 and 1589 DF, p-value: < 2.2e-16
plot(df)
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
cols = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol')
pre_proc_val <- preProcess(train[,cols], method = c("center", "scale"))
train[,cols] = predict(pre_proc_val, train[,cols])
test[,cols] = predict(pre_proc_val, test[,cols])
summary(train)
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. :-1.9104 Min. :-2.3907 Min. :-1.39209 Min. :-0.97679
## 1st Qu.:-0.7016 1st Qu.:-0.7533 1st Qu.:-0.87750 1st Qu.:-0.46632
## Median :-0.2411 Median :-0.0515 Median :-0.05417 Median :-0.24755
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.5073 3rd Qu.: 0.6502 3rd Qu.: 0.76916 3rd Qu.: 0.04415
## Max. : 4.3641 Max. : 4.6853 Max. : 3.75374 Max. : 9.37851
## chlorides free.sulfur.dioxide total.sulfur.dioxide density
## Min. :-1.57500 Min. :-1.2345 Min. :-1.2190 Min. :-3.30592
## 1st Qu.:-0.37291 1st Qu.:-0.7547 1st Qu.:-0.7434 1st Qu.:-0.62116
## Median :-0.16566 Median :-0.2748 Median :-0.2678 Median :-0.01857
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.06232 3rd Qu.: 0.4929 3rd Qu.: 0.4903 3rd Qu.: 0.58940
## Max. :10.81890 Max. : 5.0035 Max. : 7.1939 Max. : 3.71535
## pH sulphates alcohol quality
## Min. :-3.674921 Min. :-1.5199 Min. :-1.8838 Min. :3.000
## 1st Qu.:-0.637771 1st Qu.:-0.6173 1st Qu.:-0.8382 1st Qu.:5.000
## Median : 0.008431 Median :-0.2224 Median :-0.2678 Median :6.000
## Mean : 0.000000 Mean : 0.0000 Mean : 0.0000 Mean :5.627
## 3rd Qu.: 0.557703 3rd Qu.: 0.3982 3rd Qu.: 0.5877 3rd Qu.:6.000
## Max. : 4.531846 Max. : 7.5625 Max. : 4.2951 Max. :8.000
#generic LM
lm_2 <- lm(quality ~ ., data = train)
summary(lm_2)
##
## Call:
## lm(formula = quality ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.5885 -0.3492 -0.0582 0.4076 1.9578
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.62735 0.01818 309.458 < 2e-16 ***
## fixed.acidity 0.06359 0.05068 1.255 0.20987
## volatile.acidity -0.15194 0.02430 -6.252 5.78e-10 ***
## citric.acid -0.01237 0.03275 -0.378 0.70578
## residual.sugar 0.07213 0.02412 2.990 0.00285 **
## chlorides -0.09825 0.02222 -4.421 1.08e-05 ***
## free.sulfur.dioxide 0.03825 0.02567 1.490 0.13656
## total.sulfur.dioxide -0.12781 0.02697 -4.739 2.43e-06 ***
## density -0.07713 0.04582 -1.683 0.09256 .
## pH -0.05021 0.03274 -1.534 0.12542
## sulphates 0.14881 0.02174 6.843 1.28e-11 ***
## alcohol 0.26947 0.03197 8.430 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6083 on 1107 degrees of freedom
## Multiple R-squared: 0.379, Adjusted R-squared: 0.3728
## F-statistic: 61.42 on 11 and 1107 DF, p-value: < 2.2e-16
cols_reg = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol', 'quality')
dummies <- dummyVars(quality ~ ., data = df[,cols_reg])
train_dummies = predict(dummies, newdata = train[,cols_reg])
test_dummies = predict(dummies, newdata = test[,cols_reg])
print(dim(train_dummies)); print(dim(test_dummies))
## [1] 1119 11
## [1] 480 11
x = as.matrix(train_dummies)
y_train = train$quality
x_test = as.matrix(test_dummies)
y_test = test$quality
lambdas <- 10^seq(2, -3, by = -.1)
ridge_reg = glmnet(x, y_train, nlambda = 25, alpha = 0, family = 'gaussian', lambda = lambdas)
summary(ridge_reg)
## Length Class Mode
## a0 51 -none- numeric
## beta 561 dgCMatrix S4
## df 51 -none- numeric
## dim 2 -none- numeric
## lambda 51 -none- numeric
## dev.ratio 51 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numeric
cv_ridge <- cv.glmnet(x, y_train, alpha = 0, lambda = lambdas)
optimal_lambda <- cv_ridge$lambda.min
optimal_lambda
## [1] 0.05011872
# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df) {
SSE <- sum((predicted - true)^2)
SST <- sum((true - mean(true))^2)
R_square <- 1 - SSE / SST
RMSE = sqrt(SSE/nrow(df))
# Model performance metrics
data.frame(
RMSE = RMSE,
Rsquare = R_square
)
}
# Prediction and evaluation on train data
predictions_train <- predict(ridge_reg, s = optimal_lambda, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6055335 0.3779523
# Prediction and evaluation on test data
predictions_test <- predict(ridge_reg, s = optimal_lambda, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.739564 0.3132325
lambdas <- 10^seq(2, -3, by = -.1)
# Setting alpha = 1 implements lasso regression
lasso_reg <- cv.glmnet(x, y_train, alpha = 1, lambda = lambdas, standardize = TRUE, nfolds = 5)
# Best
lambda_best <- lasso_reg$lambda.min
lambda_best
## [1] 0.01258925
lasso_model <- glmnet(x, y_train, alpha = 1, lambda = lambda_best, standardize = TRUE)
predictions_train <- predict(lasso_model, s = lambda_best, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6075408 0.3738214
predictions_test <- predict(lasso_model, s = lambda_best, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.737832 0.3164453
# Set training control
train_cont <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
search = "random",
verboseIter = TRUE)
# Train the model
elastic_reg <- train(quality ~ .,
data = train,
method = "glmnet",
preProcess = c("center", "scale"),
tuneLength = 10,
trControl = train_cont)
## + Fold01.Rep1: alpha=0.3787, lambda=1.329420
## - Fold01.Rep1: alpha=0.3787, lambda=1.329420
## + Fold01.Rep1: alpha=0.1342, lambda=5.427727
## - Fold01.Rep1: alpha=0.1342, lambda=5.427727
## + Fold01.Rep1: alpha=0.4053, lambda=0.040531
## - Fold01.Rep1: alpha=0.4053, lambda=0.040531
## + Fold01.Rep1: alpha=0.9609, lambda=0.305461
## - Fold01.Rep1: alpha=0.9609, lambda=0.305461
## + Fold01.Rep1: alpha=0.1382, lambda=0.865215
## - Fold01.Rep1: alpha=0.1382, lambda=0.865215
## + Fold01.Rep1: alpha=0.8561, lambda=0.002156
## - Fold01.Rep1: alpha=0.8561, lambda=0.002156
## + Fold01.Rep1: alpha=0.4373, lambda=0.017478
## - Fold01.Rep1: alpha=0.4373, lambda=0.017478
## + Fold01.Rep1: alpha=0.1480, lambda=0.450753
## - Fold01.Rep1: alpha=0.1480, lambda=0.450753
## + Fold01.Rep1: alpha=0.8644, lambda=0.001686
## - Fold01.Rep1: alpha=0.8644, lambda=0.001686
## + Fold01.Rep1: alpha=0.1544, lambda=0.003555
## - Fold01.Rep1: alpha=0.1544, lambda=0.003555
## + Fold02.Rep1: alpha=0.3787, lambda=1.329420
## - Fold02.Rep1: alpha=0.3787, lambda=1.329420
## + Fold02.Rep1: alpha=0.1342, lambda=5.427727
## - Fold02.Rep1: alpha=0.1342, lambda=5.427727
## + Fold02.Rep1: alpha=0.4053, lambda=0.040531
## - Fold02.Rep1: alpha=0.4053, lambda=0.040531
## + Fold02.Rep1: alpha=0.9609, lambda=0.305461
## - Fold02.Rep1: alpha=0.9609, lambda=0.305461
## + Fold02.Rep1: alpha=0.1382, lambda=0.865215
## - Fold02.Rep1: alpha=0.1382, lambda=0.865215
## + Fold02.Rep1: alpha=0.8561, lambda=0.002156
## - Fold02.Rep1: alpha=0.8561, lambda=0.002156
## + Fold02.Rep1: alpha=0.4373, lambda=0.017478
## - Fold02.Rep1: alpha=0.4373, lambda=0.017478
## + Fold02.Rep1: alpha=0.1480, lambda=0.450753
## - Fold02.Rep1: alpha=0.1480, lambda=0.450753
## + Fold02.Rep1: alpha=0.8644, lambda=0.001686
## - Fold02.Rep1: alpha=0.8644, lambda=0.001686
## + Fold02.Rep1: alpha=0.1544, lambda=0.003555
## - Fold02.Rep1: alpha=0.1544, lambda=0.003555
## + Fold03.Rep1: alpha=0.3787, lambda=1.329420
## - Fold03.Rep1: alpha=0.3787, lambda=1.329420
## + Fold03.Rep1: alpha=0.1342, lambda=5.427727
## - Fold03.Rep1: alpha=0.1342, lambda=5.427727
## + Fold03.Rep1: alpha=0.4053, lambda=0.040531
## - Fold03.Rep1: alpha=0.4053, lambda=0.040531
## + Fold03.Rep1: alpha=0.9609, lambda=0.305461
## - Fold03.Rep1: alpha=0.9609, lambda=0.305461
## + Fold03.Rep1: alpha=0.1382, lambda=0.865215
## - Fold03.Rep1: alpha=0.1382, lambda=0.865215
## + Fold03.Rep1: alpha=0.8561, lambda=0.002156
## - Fold03.Rep1: alpha=0.8561, lambda=0.002156
## + Fold03.Rep1: alpha=0.4373, lambda=0.017478
## - Fold03.Rep1: alpha=0.4373, lambda=0.017478
## + Fold03.Rep1: alpha=0.1480, lambda=0.450753
## - Fold03.Rep1: alpha=0.1480, lambda=0.450753
## + Fold03.Rep1: alpha=0.8644, lambda=0.001686
## - Fold03.Rep1: alpha=0.8644, lambda=0.001686
## + Fold03.Rep1: alpha=0.1544, lambda=0.003555
## - Fold03.Rep1: alpha=0.1544, lambda=0.003555
## + Fold04.Rep1: alpha=0.3787, lambda=1.329420
## - Fold04.Rep1: alpha=0.3787, lambda=1.329420
## + Fold04.Rep1: alpha=0.1342, lambda=5.427727
## - Fold04.Rep1: alpha=0.1342, lambda=5.427727
## + Fold04.Rep1: alpha=0.4053, lambda=0.040531
## - Fold04.Rep1: alpha=0.4053, lambda=0.040531
## + Fold04.Rep1: alpha=0.9609, lambda=0.305461
## - Fold04.Rep1: alpha=0.9609, lambda=0.305461
## + Fold04.Rep1: alpha=0.1382, lambda=0.865215
## - Fold04.Rep1: alpha=0.1382, lambda=0.865215
## + Fold04.Rep1: alpha=0.8561, lambda=0.002156
## - Fold04.Rep1: alpha=0.8561, lambda=0.002156
## + Fold04.Rep1: alpha=0.4373, lambda=0.017478
## - Fold04.Rep1: alpha=0.4373, lambda=0.017478
## + Fold04.Rep1: alpha=0.1480, lambda=0.450753
## - Fold04.Rep1: alpha=0.1480, lambda=0.450753
## + Fold04.Rep1: alpha=0.8644, lambda=0.001686
## - Fold04.Rep1: alpha=0.8644, lambda=0.001686
## + Fold04.Rep1: alpha=0.1544, lambda=0.003555
## - Fold04.Rep1: alpha=0.1544, lambda=0.003555
## + Fold05.Rep1: alpha=0.3787, lambda=1.329420
## - Fold05.Rep1: alpha=0.3787, lambda=1.329420
## + Fold05.Rep1: alpha=0.1342, lambda=5.427727
## - Fold05.Rep1: alpha=0.1342, lambda=5.427727
## + Fold05.Rep1: alpha=0.4053, lambda=0.040531
## - Fold05.Rep1: alpha=0.4053, lambda=0.040531
## + Fold05.Rep1: alpha=0.9609, lambda=0.305461
## - Fold05.Rep1: alpha=0.9609, lambda=0.305461
## + Fold05.Rep1: alpha=0.1382, lambda=0.865215
## - Fold05.Rep1: alpha=0.1382, lambda=0.865215
## + Fold05.Rep1: alpha=0.8561, lambda=0.002156
## - Fold05.Rep1: alpha=0.8561, lambda=0.002156
## + Fold05.Rep1: alpha=0.4373, lambda=0.017478
## - Fold05.Rep1: alpha=0.4373, lambda=0.017478
## + Fold05.Rep1: alpha=0.1480, lambda=0.450753
## - Fold05.Rep1: alpha=0.1480, lambda=0.450753
## + Fold05.Rep1: alpha=0.8644, lambda=0.001686
## - Fold05.Rep1: alpha=0.8644, lambda=0.001686
## + Fold05.Rep1: alpha=0.1544, lambda=0.003555
## - Fold05.Rep1: alpha=0.1544, lambda=0.003555
## + Fold06.Rep1: alpha=0.3787, lambda=1.329420
## - Fold06.Rep1: alpha=0.3787, lambda=1.329420
## + Fold06.Rep1: alpha=0.1342, lambda=5.427727
## - Fold06.Rep1: alpha=0.1342, lambda=5.427727
## + Fold06.Rep1: alpha=0.4053, lambda=0.040531
## - Fold06.Rep1: alpha=0.4053, lambda=0.040531
## + Fold06.Rep1: alpha=0.9609, lambda=0.305461
## - Fold06.Rep1: alpha=0.9609, lambda=0.305461
## + Fold06.Rep1: alpha=0.1382, lambda=0.865215
## - Fold06.Rep1: alpha=0.1382, lambda=0.865215
## + Fold06.Rep1: alpha=0.8561, lambda=0.002156
## - Fold06.Rep1: alpha=0.8561, lambda=0.002156
## + Fold06.Rep1: alpha=0.4373, lambda=0.017478
## - Fold06.Rep1: alpha=0.4373, lambda=0.017478
## + Fold06.Rep1: alpha=0.1480, lambda=0.450753
## - Fold06.Rep1: alpha=0.1480, lambda=0.450753
## + Fold06.Rep1: alpha=0.8644, lambda=0.001686
## - Fold06.Rep1: alpha=0.8644, lambda=0.001686
## + Fold06.Rep1: alpha=0.1544, lambda=0.003555
## - Fold06.Rep1: alpha=0.1544, lambda=0.003555
## + Fold07.Rep1: alpha=0.3787, lambda=1.329420
## - Fold07.Rep1: alpha=0.3787, lambda=1.329420
## + Fold07.Rep1: alpha=0.1342, lambda=5.427727
## - Fold07.Rep1: alpha=0.1342, lambda=5.427727
## + Fold07.Rep1: alpha=0.4053, lambda=0.040531
## - Fold07.Rep1: alpha=0.4053, lambda=0.040531
## + Fold07.Rep1: alpha=0.9609, lambda=0.305461
## - Fold07.Rep1: alpha=0.9609, lambda=0.305461
## + Fold07.Rep1: alpha=0.1382, lambda=0.865215
## - Fold07.Rep1: alpha=0.1382, lambda=0.865215
## + Fold07.Rep1: alpha=0.8561, lambda=0.002156
## - Fold07.Rep1: alpha=0.8561, lambda=0.002156
## + Fold07.Rep1: alpha=0.4373, lambda=0.017478
## - Fold07.Rep1: alpha=0.4373, lambda=0.017478
## + Fold07.Rep1: alpha=0.1480, lambda=0.450753
## - Fold07.Rep1: alpha=0.1480, lambda=0.450753
## + Fold07.Rep1: alpha=0.8644, lambda=0.001686
## - Fold07.Rep1: alpha=0.8644, lambda=0.001686
## + Fold07.Rep1: alpha=0.1544, lambda=0.003555
## - Fold07.Rep1: alpha=0.1544, lambda=0.003555
## + Fold08.Rep1: alpha=0.3787, lambda=1.329420
## - Fold08.Rep1: alpha=0.3787, lambda=1.329420
## + Fold08.Rep1: alpha=0.1342, lambda=5.427727
## - Fold08.Rep1: alpha=0.1342, lambda=5.427727
## + Fold08.Rep1: alpha=0.4053, lambda=0.040531
## - Fold08.Rep1: alpha=0.4053, lambda=0.040531
## + Fold08.Rep1: alpha=0.9609, lambda=0.305461
## - Fold08.Rep1: alpha=0.9609, lambda=0.305461
## + Fold08.Rep1: alpha=0.1382, lambda=0.865215
## - Fold08.Rep1: alpha=0.1382, lambda=0.865215
## + Fold08.Rep1: alpha=0.8561, lambda=0.002156
## - Fold08.Rep1: alpha=0.8561, lambda=0.002156
## + Fold08.Rep1: alpha=0.4373, lambda=0.017478
## - Fold08.Rep1: alpha=0.4373, lambda=0.017478
## + Fold08.Rep1: alpha=0.1480, lambda=0.450753
## - Fold08.Rep1: alpha=0.1480, lambda=0.450753
## + Fold08.Rep1: alpha=0.8644, lambda=0.001686
## - Fold08.Rep1: alpha=0.8644, lambda=0.001686
## + Fold08.Rep1: alpha=0.1544, lambda=0.003555
## - Fold08.Rep1: alpha=0.1544, lambda=0.003555
## + Fold09.Rep1: alpha=0.3787, lambda=1.329420
## - Fold09.Rep1: alpha=0.3787, lambda=1.329420
## + Fold09.Rep1: alpha=0.1342, lambda=5.427727
## - Fold09.Rep1: alpha=0.1342, lambda=5.427727
## + Fold09.Rep1: alpha=0.4053, lambda=0.040531
## - Fold09.Rep1: alpha=0.4053, lambda=0.040531
## + Fold09.Rep1: alpha=0.9609, lambda=0.305461
## - Fold09.Rep1: alpha=0.9609, lambda=0.305461
## + Fold09.Rep1: alpha=0.1382, lambda=0.865215
## - Fold09.Rep1: alpha=0.1382, lambda=0.865215
## + Fold09.Rep1: alpha=0.8561, lambda=0.002156
## - Fold09.Rep1: alpha=0.8561, lambda=0.002156
## + Fold09.Rep1: alpha=0.4373, lambda=0.017478
## - Fold09.Rep1: alpha=0.4373, lambda=0.017478
## + Fold09.Rep1: alpha=0.1480, lambda=0.450753
## - Fold09.Rep1: alpha=0.1480, lambda=0.450753
## + Fold09.Rep1: alpha=0.8644, lambda=0.001686
## - Fold09.Rep1: alpha=0.8644, lambda=0.001686
## + Fold09.Rep1: alpha=0.1544, lambda=0.003555
## - Fold09.Rep1: alpha=0.1544, lambda=0.003555
## + Fold10.Rep1: alpha=0.3787, lambda=1.329420
## - Fold10.Rep1: alpha=0.3787, lambda=1.329420
## + Fold10.Rep1: alpha=0.1342, lambda=5.427727
## - Fold10.Rep1: alpha=0.1342, lambda=5.427727
## + Fold10.Rep1: alpha=0.4053, lambda=0.040531
## - Fold10.Rep1: alpha=0.4053, lambda=0.040531
## + Fold10.Rep1: alpha=0.9609, lambda=0.305461
## - Fold10.Rep1: alpha=0.9609, lambda=0.305461
## + Fold10.Rep1: alpha=0.1382, lambda=0.865215
## - Fold10.Rep1: alpha=0.1382, lambda=0.865215
## + Fold10.Rep1: alpha=0.8561, lambda=0.002156
## - Fold10.Rep1: alpha=0.8561, lambda=0.002156
## + Fold10.Rep1: alpha=0.4373, lambda=0.017478
## - Fold10.Rep1: alpha=0.4373, lambda=0.017478
## + Fold10.Rep1: alpha=0.1480, lambda=0.450753
## - Fold10.Rep1: alpha=0.1480, lambda=0.450753
## + Fold10.Rep1: alpha=0.8644, lambda=0.001686
## - Fold10.Rep1: alpha=0.8644, lambda=0.001686
## + Fold10.Rep1: alpha=0.1544, lambda=0.003555
## - Fold10.Rep1: alpha=0.1544, lambda=0.003555
## + Fold01.Rep2: alpha=0.3787, lambda=1.329420
## - Fold01.Rep2: alpha=0.3787, lambda=1.329420
## + Fold01.Rep2: alpha=0.1342, lambda=5.427727
## - Fold01.Rep2: alpha=0.1342, lambda=5.427727
## + Fold01.Rep2: alpha=0.4053, lambda=0.040531
## - Fold01.Rep2: alpha=0.4053, lambda=0.040531
## + Fold01.Rep2: alpha=0.9609, lambda=0.305461
## - Fold01.Rep2: alpha=0.9609, lambda=0.305461
## + Fold01.Rep2: alpha=0.1382, lambda=0.865215
## - Fold01.Rep2: alpha=0.1382, lambda=0.865215
## + Fold01.Rep2: alpha=0.8561, lambda=0.002156
## - Fold01.Rep2: alpha=0.8561, lambda=0.002156
## + Fold01.Rep2: alpha=0.4373, lambda=0.017478
## - Fold01.Rep2: alpha=0.4373, lambda=0.017478
## + Fold01.Rep2: alpha=0.1480, lambda=0.450753
## - Fold01.Rep2: alpha=0.1480, lambda=0.450753
## + Fold01.Rep2: alpha=0.8644, lambda=0.001686
## - Fold01.Rep2: alpha=0.8644, lambda=0.001686
## + Fold01.Rep2: alpha=0.1544, lambda=0.003555
## - Fold01.Rep2: alpha=0.1544, lambda=0.003555
## + Fold02.Rep2: alpha=0.3787, lambda=1.329420
## - Fold02.Rep2: alpha=0.3787, lambda=1.329420
## + Fold02.Rep2: alpha=0.1342, lambda=5.427727
## - Fold02.Rep2: alpha=0.1342, lambda=5.427727
## + Fold02.Rep2: alpha=0.4053, lambda=0.040531
## - Fold02.Rep2: alpha=0.4053, lambda=0.040531
## + Fold02.Rep2: alpha=0.9609, lambda=0.305461
## - Fold02.Rep2: alpha=0.9609, lambda=0.305461
## + Fold02.Rep2: alpha=0.1382, lambda=0.865215
## - Fold02.Rep2: alpha=0.1382, lambda=0.865215
## + Fold02.Rep2: alpha=0.8561, lambda=0.002156
## - Fold02.Rep2: alpha=0.8561, lambda=0.002156
## + Fold02.Rep2: alpha=0.4373, lambda=0.017478
## - Fold02.Rep2: alpha=0.4373, lambda=0.017478
## + Fold02.Rep2: alpha=0.1480, lambda=0.450753
## - Fold02.Rep2: alpha=0.1480, lambda=0.450753
## + Fold02.Rep2: alpha=0.8644, lambda=0.001686
## - Fold02.Rep2: alpha=0.8644, lambda=0.001686
## + Fold02.Rep2: alpha=0.1544, lambda=0.003555
## - Fold02.Rep2: alpha=0.1544, lambda=0.003555
## + Fold03.Rep2: alpha=0.3787, lambda=1.329420
## - Fold03.Rep2: alpha=0.3787, lambda=1.329420
## + Fold03.Rep2: alpha=0.1342, lambda=5.427727
## - Fold03.Rep2: alpha=0.1342, lambda=5.427727
## + Fold03.Rep2: alpha=0.4053, lambda=0.040531
## - Fold03.Rep2: alpha=0.4053, lambda=0.040531
## + Fold03.Rep2: alpha=0.9609, lambda=0.305461
## - Fold03.Rep2: alpha=0.9609, lambda=0.305461
## + Fold03.Rep2: alpha=0.1382, lambda=0.865215
## - Fold03.Rep2: alpha=0.1382, lambda=0.865215
## + Fold03.Rep2: alpha=0.8561, lambda=0.002156
## - Fold03.Rep2: alpha=0.8561, lambda=0.002156
## + Fold03.Rep2: alpha=0.4373, lambda=0.017478
## - Fold03.Rep2: alpha=0.4373, lambda=0.017478
## + Fold03.Rep2: alpha=0.1480, lambda=0.450753
## - Fold03.Rep2: alpha=0.1480, lambda=0.450753
## + Fold03.Rep2: alpha=0.8644, lambda=0.001686
## - Fold03.Rep2: alpha=0.8644, lambda=0.001686
## + Fold03.Rep2: alpha=0.1544, lambda=0.003555
## - Fold03.Rep2: alpha=0.1544, lambda=0.003555
## + Fold04.Rep2: alpha=0.3787, lambda=1.329420
## - Fold04.Rep2: alpha=0.3787, lambda=1.329420
## + Fold04.Rep2: alpha=0.1342, lambda=5.427727
## - Fold04.Rep2: alpha=0.1342, lambda=5.427727
## + Fold04.Rep2: alpha=0.4053, lambda=0.040531
## - Fold04.Rep2: alpha=0.4053, lambda=0.040531
## + Fold04.Rep2: alpha=0.9609, lambda=0.305461
## - Fold04.Rep2: alpha=0.9609, lambda=0.305461
## + Fold04.Rep2: alpha=0.1382, lambda=0.865215
## - Fold04.Rep2: alpha=0.1382, lambda=0.865215
## + Fold04.Rep2: alpha=0.8561, lambda=0.002156
## - Fold04.Rep2: alpha=0.8561, lambda=0.002156
## + Fold04.Rep2: alpha=0.4373, lambda=0.017478
## - Fold04.Rep2: alpha=0.4373, lambda=0.017478
## + Fold04.Rep2: alpha=0.1480, lambda=0.450753
## - Fold04.Rep2: alpha=0.1480, lambda=0.450753
## + Fold04.Rep2: alpha=0.8644, lambda=0.001686
## - Fold04.Rep2: alpha=0.8644, lambda=0.001686
## + Fold04.Rep2: alpha=0.1544, lambda=0.003555
## - Fold04.Rep2: alpha=0.1544, lambda=0.003555
## + Fold05.Rep2: alpha=0.3787, lambda=1.329420
## - Fold05.Rep2: alpha=0.3787, lambda=1.329420
## + Fold05.Rep2: alpha=0.1342, lambda=5.427727
## - Fold05.Rep2: alpha=0.1342, lambda=5.427727
## + Fold05.Rep2: alpha=0.4053, lambda=0.040531
## - Fold05.Rep2: alpha=0.4053, lambda=0.040531
## + Fold05.Rep2: alpha=0.9609, lambda=0.305461
## - Fold05.Rep2: alpha=0.9609, lambda=0.305461
## + Fold05.Rep2: alpha=0.1382, lambda=0.865215
## - Fold05.Rep2: alpha=0.1382, lambda=0.865215
## + Fold05.Rep2: alpha=0.8561, lambda=0.002156
## - Fold05.Rep2: alpha=0.8561, lambda=0.002156
## + Fold05.Rep2: alpha=0.4373, lambda=0.017478
## - Fold05.Rep2: alpha=0.4373, lambda=0.017478
## + Fold05.Rep2: alpha=0.1480, lambda=0.450753
## - Fold05.Rep2: alpha=0.1480, lambda=0.450753
## + Fold05.Rep2: alpha=0.8644, lambda=0.001686
## - Fold05.Rep2: alpha=0.8644, lambda=0.001686
## + Fold05.Rep2: alpha=0.1544, lambda=0.003555
## - Fold05.Rep2: alpha=0.1544, lambda=0.003555
## + Fold06.Rep2: alpha=0.3787, lambda=1.329420
## - Fold06.Rep2: alpha=0.3787, lambda=1.329420
## + Fold06.Rep2: alpha=0.1342, lambda=5.427727
## - Fold06.Rep2: alpha=0.1342, lambda=5.427727
## + Fold06.Rep2: alpha=0.4053, lambda=0.040531
## - Fold06.Rep2: alpha=0.4053, lambda=0.040531
## + Fold06.Rep2: alpha=0.9609, lambda=0.305461
## - Fold06.Rep2: alpha=0.9609, lambda=0.305461
## + Fold06.Rep2: alpha=0.1382, lambda=0.865215
## - Fold06.Rep2: alpha=0.1382, lambda=0.865215
## + Fold06.Rep2: alpha=0.8561, lambda=0.002156
## - Fold06.Rep2: alpha=0.8561, lambda=0.002156
## + Fold06.Rep2: alpha=0.4373, lambda=0.017478
## - Fold06.Rep2: alpha=0.4373, lambda=0.017478
## + Fold06.Rep2: alpha=0.1480, lambda=0.450753
## - Fold06.Rep2: alpha=0.1480, lambda=0.450753
## + Fold06.Rep2: alpha=0.8644, lambda=0.001686
## - Fold06.Rep2: alpha=0.8644, lambda=0.001686
## + Fold06.Rep2: alpha=0.1544, lambda=0.003555
## - Fold06.Rep2: alpha=0.1544, lambda=0.003555
## + Fold07.Rep2: alpha=0.3787, lambda=1.329420
## - Fold07.Rep2: alpha=0.3787, lambda=1.329420
## + Fold07.Rep2: alpha=0.1342, lambda=5.427727
## - Fold07.Rep2: alpha=0.1342, lambda=5.427727
## + Fold07.Rep2: alpha=0.4053, lambda=0.040531
## - Fold07.Rep2: alpha=0.4053, lambda=0.040531
## + Fold07.Rep2: alpha=0.9609, lambda=0.305461
## - Fold07.Rep2: alpha=0.9609, lambda=0.305461
## + Fold07.Rep2: alpha=0.1382, lambda=0.865215
## - Fold07.Rep2: alpha=0.1382, lambda=0.865215
## + Fold07.Rep2: alpha=0.8561, lambda=0.002156
## - Fold07.Rep2: alpha=0.8561, lambda=0.002156
## + Fold07.Rep2: alpha=0.4373, lambda=0.017478
## - Fold07.Rep2: alpha=0.4373, lambda=0.017478
## + Fold07.Rep2: alpha=0.1480, lambda=0.450753
## - Fold07.Rep2: alpha=0.1480, lambda=0.450753
## + Fold07.Rep2: alpha=0.8644, lambda=0.001686
## - Fold07.Rep2: alpha=0.8644, lambda=0.001686
## + Fold07.Rep2: alpha=0.1544, lambda=0.003555
## - Fold07.Rep2: alpha=0.1544, lambda=0.003555
## + Fold08.Rep2: alpha=0.3787, lambda=1.329420
## - Fold08.Rep2: alpha=0.3787, lambda=1.329420
## + Fold08.Rep2: alpha=0.1342, lambda=5.427727
## - Fold08.Rep2: alpha=0.1342, lambda=5.427727
## + Fold08.Rep2: alpha=0.4053, lambda=0.040531
## - Fold08.Rep2: alpha=0.4053, lambda=0.040531
## + Fold08.Rep2: alpha=0.9609, lambda=0.305461
## - Fold08.Rep2: alpha=0.9609, lambda=0.305461
## + Fold08.Rep2: alpha=0.1382, lambda=0.865215
## - Fold08.Rep2: alpha=0.1382, lambda=0.865215
## + Fold08.Rep2: alpha=0.8561, lambda=0.002156
## - Fold08.Rep2: alpha=0.8561, lambda=0.002156
## + Fold08.Rep2: alpha=0.4373, lambda=0.017478
## - Fold08.Rep2: alpha=0.4373, lambda=0.017478
## + Fold08.Rep2: alpha=0.1480, lambda=0.450753
## - Fold08.Rep2: alpha=0.1480, lambda=0.450753
## + Fold08.Rep2: alpha=0.8644, lambda=0.001686
## - Fold08.Rep2: alpha=0.8644, lambda=0.001686
## + Fold08.Rep2: alpha=0.1544, lambda=0.003555
## - Fold08.Rep2: alpha=0.1544, lambda=0.003555
## + Fold09.Rep2: alpha=0.3787, lambda=1.329420
## - Fold09.Rep2: alpha=0.3787, lambda=1.329420
## + Fold09.Rep2: alpha=0.1342, lambda=5.427727
## - Fold09.Rep2: alpha=0.1342, lambda=5.427727
## + Fold09.Rep2: alpha=0.4053, lambda=0.040531
## - Fold09.Rep2: alpha=0.4053, lambda=0.040531
## + Fold09.Rep2: alpha=0.9609, lambda=0.305461
## - Fold09.Rep2: alpha=0.9609, lambda=0.305461
## + Fold09.Rep2: alpha=0.1382, lambda=0.865215
## - Fold09.Rep2: alpha=0.1382, lambda=0.865215
## + Fold09.Rep2: alpha=0.8561, lambda=0.002156
## - Fold09.Rep2: alpha=0.8561, lambda=0.002156
## + Fold09.Rep2: alpha=0.4373, lambda=0.017478
## - Fold09.Rep2: alpha=0.4373, lambda=0.017478
## + Fold09.Rep2: alpha=0.1480, lambda=0.450753
## - Fold09.Rep2: alpha=0.1480, lambda=0.450753
## + Fold09.Rep2: alpha=0.8644, lambda=0.001686
## - Fold09.Rep2: alpha=0.8644, lambda=0.001686
## + Fold09.Rep2: alpha=0.1544, lambda=0.003555
## - Fold09.Rep2: alpha=0.1544, lambda=0.003555
## + Fold10.Rep2: alpha=0.3787, lambda=1.329420
## - Fold10.Rep2: alpha=0.3787, lambda=1.329420
## + Fold10.Rep2: alpha=0.1342, lambda=5.427727
## - Fold10.Rep2: alpha=0.1342, lambda=5.427727
## + Fold10.Rep2: alpha=0.4053, lambda=0.040531
## - Fold10.Rep2: alpha=0.4053, lambda=0.040531
## + Fold10.Rep2: alpha=0.9609, lambda=0.305461
## - Fold10.Rep2: alpha=0.9609, lambda=0.305461
## + Fold10.Rep2: alpha=0.1382, lambda=0.865215
## - Fold10.Rep2: alpha=0.1382, lambda=0.865215
## + Fold10.Rep2: alpha=0.8561, lambda=0.002156
## - Fold10.Rep2: alpha=0.8561, lambda=0.002156
## + Fold10.Rep2: alpha=0.4373, lambda=0.017478
## - Fold10.Rep2: alpha=0.4373, lambda=0.017478
## + Fold10.Rep2: alpha=0.1480, lambda=0.450753
## - Fold10.Rep2: alpha=0.1480, lambda=0.450753
## + Fold10.Rep2: alpha=0.8644, lambda=0.001686
## - Fold10.Rep2: alpha=0.8644, lambda=0.001686
## + Fold10.Rep2: alpha=0.1544, lambda=0.003555
## - Fold10.Rep2: alpha=0.1544, lambda=0.003555
## + Fold01.Rep3: alpha=0.3787, lambda=1.329420
## - Fold01.Rep3: alpha=0.3787, lambda=1.329420
## + Fold01.Rep3: alpha=0.1342, lambda=5.427727
## - Fold01.Rep3: alpha=0.1342, lambda=5.427727
## + Fold01.Rep3: alpha=0.4053, lambda=0.040531
## - Fold01.Rep3: alpha=0.4053, lambda=0.040531
## + Fold01.Rep3: alpha=0.9609, lambda=0.305461
## - Fold01.Rep3: alpha=0.9609, lambda=0.305461
## + Fold01.Rep3: alpha=0.1382, lambda=0.865215
## - Fold01.Rep3: alpha=0.1382, lambda=0.865215
## + Fold01.Rep3: alpha=0.8561, lambda=0.002156
## - Fold01.Rep3: alpha=0.8561, lambda=0.002156
## + Fold01.Rep3: alpha=0.4373, lambda=0.017478
## - Fold01.Rep3: alpha=0.4373, lambda=0.017478
## + Fold01.Rep3: alpha=0.1480, lambda=0.450753
## - Fold01.Rep3: alpha=0.1480, lambda=0.450753
## + Fold01.Rep3: alpha=0.8644, lambda=0.001686
## - Fold01.Rep3: alpha=0.8644, lambda=0.001686
## + Fold01.Rep3: alpha=0.1544, lambda=0.003555
## - Fold01.Rep3: alpha=0.1544, lambda=0.003555
## + Fold02.Rep3: alpha=0.3787, lambda=1.329420
## - Fold02.Rep3: alpha=0.3787, lambda=1.329420
## + Fold02.Rep3: alpha=0.1342, lambda=5.427727
## - Fold02.Rep3: alpha=0.1342, lambda=5.427727
## + Fold02.Rep3: alpha=0.4053, lambda=0.040531
## - Fold02.Rep3: alpha=0.4053, lambda=0.040531
## + Fold02.Rep3: alpha=0.9609, lambda=0.305461
## - Fold02.Rep3: alpha=0.9609, lambda=0.305461
## + Fold02.Rep3: alpha=0.1382, lambda=0.865215
## - Fold02.Rep3: alpha=0.1382, lambda=0.865215
## + Fold02.Rep3: alpha=0.8561, lambda=0.002156
## - Fold02.Rep3: alpha=0.8561, lambda=0.002156
## + Fold02.Rep3: alpha=0.4373, lambda=0.017478
## - Fold02.Rep3: alpha=0.4373, lambda=0.017478
## + Fold02.Rep3: alpha=0.1480, lambda=0.450753
## - Fold02.Rep3: alpha=0.1480, lambda=0.450753
## + Fold02.Rep3: alpha=0.8644, lambda=0.001686
## - Fold02.Rep3: alpha=0.8644, lambda=0.001686
## + Fold02.Rep3: alpha=0.1544, lambda=0.003555
## - Fold02.Rep3: alpha=0.1544, lambda=0.003555
## + Fold03.Rep3: alpha=0.3787, lambda=1.329420
## - Fold03.Rep3: alpha=0.3787, lambda=1.329420
## + Fold03.Rep3: alpha=0.1342, lambda=5.427727
## - Fold03.Rep3: alpha=0.1342, lambda=5.427727
## + Fold03.Rep3: alpha=0.4053, lambda=0.040531
## - Fold03.Rep3: alpha=0.4053, lambda=0.040531
## + Fold03.Rep3: alpha=0.9609, lambda=0.305461
## - Fold03.Rep3: alpha=0.9609, lambda=0.305461
## + Fold03.Rep3: alpha=0.1382, lambda=0.865215
## - Fold03.Rep3: alpha=0.1382, lambda=0.865215
## + Fold03.Rep3: alpha=0.8561, lambda=0.002156
## - Fold03.Rep3: alpha=0.8561, lambda=0.002156
## + Fold03.Rep3: alpha=0.4373, lambda=0.017478
## - Fold03.Rep3: alpha=0.4373, lambda=0.017478
## + Fold03.Rep3: alpha=0.1480, lambda=0.450753
## - Fold03.Rep3: alpha=0.1480, lambda=0.450753
## + Fold03.Rep3: alpha=0.8644, lambda=0.001686
## - Fold03.Rep3: alpha=0.8644, lambda=0.001686
## + Fold03.Rep3: alpha=0.1544, lambda=0.003555
## - Fold03.Rep3: alpha=0.1544, lambda=0.003555
## + Fold04.Rep3: alpha=0.3787, lambda=1.329420
## - Fold04.Rep3: alpha=0.3787, lambda=1.329420
## + Fold04.Rep3: alpha=0.1342, lambda=5.427727
## - Fold04.Rep3: alpha=0.1342, lambda=5.427727
## + Fold04.Rep3: alpha=0.4053, lambda=0.040531
## - Fold04.Rep3: alpha=0.4053, lambda=0.040531
## + Fold04.Rep3: alpha=0.9609, lambda=0.305461
## - Fold04.Rep3: alpha=0.9609, lambda=0.305461
## + Fold04.Rep3: alpha=0.1382, lambda=0.865215
## - Fold04.Rep3: alpha=0.1382, lambda=0.865215
## + Fold04.Rep3: alpha=0.8561, lambda=0.002156
## - Fold04.Rep3: alpha=0.8561, lambda=0.002156
## + Fold04.Rep3: alpha=0.4373, lambda=0.017478
## - Fold04.Rep3: alpha=0.4373, lambda=0.017478
## + Fold04.Rep3: alpha=0.1480, lambda=0.450753
## - Fold04.Rep3: alpha=0.1480, lambda=0.450753
## + Fold04.Rep3: alpha=0.8644, lambda=0.001686
## - Fold04.Rep3: alpha=0.8644, lambda=0.001686
## + Fold04.Rep3: alpha=0.1544, lambda=0.003555
## - Fold04.Rep3: alpha=0.1544, lambda=0.003555
## + Fold05.Rep3: alpha=0.3787, lambda=1.329420
## - Fold05.Rep3: alpha=0.3787, lambda=1.329420
## + Fold05.Rep3: alpha=0.1342, lambda=5.427727
## - Fold05.Rep3: alpha=0.1342, lambda=5.427727
## + Fold05.Rep3: alpha=0.4053, lambda=0.040531
## - Fold05.Rep3: alpha=0.4053, lambda=0.040531
## + Fold05.Rep3: alpha=0.9609, lambda=0.305461
## - Fold05.Rep3: alpha=0.9609, lambda=0.305461
## + Fold05.Rep3: alpha=0.1382, lambda=0.865215
## - Fold05.Rep3: alpha=0.1382, lambda=0.865215
## + Fold05.Rep3: alpha=0.8561, lambda=0.002156
## - Fold05.Rep3: alpha=0.8561, lambda=0.002156
## + Fold05.Rep3: alpha=0.4373, lambda=0.017478
## - Fold05.Rep3: alpha=0.4373, lambda=0.017478
## + Fold05.Rep3: alpha=0.1480, lambda=0.450753
## - Fold05.Rep3: alpha=0.1480, lambda=0.450753
## + Fold05.Rep3: alpha=0.8644, lambda=0.001686
## - Fold05.Rep3: alpha=0.8644, lambda=0.001686
## + Fold05.Rep3: alpha=0.1544, lambda=0.003555
## - Fold05.Rep3: alpha=0.1544, lambda=0.003555
## + Fold06.Rep3: alpha=0.3787, lambda=1.329420
## - Fold06.Rep3: alpha=0.3787, lambda=1.329420
## + Fold06.Rep3: alpha=0.1342, lambda=5.427727
## - Fold06.Rep3: alpha=0.1342, lambda=5.427727
## + Fold06.Rep3: alpha=0.4053, lambda=0.040531
## - Fold06.Rep3: alpha=0.4053, lambda=0.040531
## + Fold06.Rep3: alpha=0.9609, lambda=0.305461
## - Fold06.Rep3: alpha=0.9609, lambda=0.305461
## + Fold06.Rep3: alpha=0.1382, lambda=0.865215
## - Fold06.Rep3: alpha=0.1382, lambda=0.865215
## + Fold06.Rep3: alpha=0.8561, lambda=0.002156
## - Fold06.Rep3: alpha=0.8561, lambda=0.002156
## + Fold06.Rep3: alpha=0.4373, lambda=0.017478
## - Fold06.Rep3: alpha=0.4373, lambda=0.017478
## + Fold06.Rep3: alpha=0.1480, lambda=0.450753
## - Fold06.Rep3: alpha=0.1480, lambda=0.450753
## + Fold06.Rep3: alpha=0.8644, lambda=0.001686
## - Fold06.Rep3: alpha=0.8644, lambda=0.001686
## + Fold06.Rep3: alpha=0.1544, lambda=0.003555
## - Fold06.Rep3: alpha=0.1544, lambda=0.003555
## + Fold07.Rep3: alpha=0.3787, lambda=1.329420
## - Fold07.Rep3: alpha=0.3787, lambda=1.329420
## + Fold07.Rep3: alpha=0.1342, lambda=5.427727
## - Fold07.Rep3: alpha=0.1342, lambda=5.427727
## + Fold07.Rep3: alpha=0.4053, lambda=0.040531
## - Fold07.Rep3: alpha=0.4053, lambda=0.040531
## + Fold07.Rep3: alpha=0.9609, lambda=0.305461
## - Fold07.Rep3: alpha=0.9609, lambda=0.305461
## + Fold07.Rep3: alpha=0.1382, lambda=0.865215
## - Fold07.Rep3: alpha=0.1382, lambda=0.865215
## + Fold07.Rep3: alpha=0.8561, lambda=0.002156
## - Fold07.Rep3: alpha=0.8561, lambda=0.002156
## + Fold07.Rep3: alpha=0.4373, lambda=0.017478
## - Fold07.Rep3: alpha=0.4373, lambda=0.017478
## + Fold07.Rep3: alpha=0.1480, lambda=0.450753
## - Fold07.Rep3: alpha=0.1480, lambda=0.450753
## + Fold07.Rep3: alpha=0.8644, lambda=0.001686
## - Fold07.Rep3: alpha=0.8644, lambda=0.001686
## + Fold07.Rep3: alpha=0.1544, lambda=0.003555
## - Fold07.Rep3: alpha=0.1544, lambda=0.003555
## + Fold08.Rep3: alpha=0.3787, lambda=1.329420
## - Fold08.Rep3: alpha=0.3787, lambda=1.329420
## + Fold08.Rep3: alpha=0.1342, lambda=5.427727
## - Fold08.Rep3: alpha=0.1342, lambda=5.427727
## + Fold08.Rep3: alpha=0.4053, lambda=0.040531
## - Fold08.Rep3: alpha=0.4053, lambda=0.040531
## + Fold08.Rep3: alpha=0.9609, lambda=0.305461
## - Fold08.Rep3: alpha=0.9609, lambda=0.305461
## + Fold08.Rep3: alpha=0.1382, lambda=0.865215
## - Fold08.Rep3: alpha=0.1382, lambda=0.865215
## + Fold08.Rep3: alpha=0.8561, lambda=0.002156
## - Fold08.Rep3: alpha=0.8561, lambda=0.002156
## + Fold08.Rep3: alpha=0.4373, lambda=0.017478
## - Fold08.Rep3: alpha=0.4373, lambda=0.017478
## + Fold08.Rep3: alpha=0.1480, lambda=0.450753
## - Fold08.Rep3: alpha=0.1480, lambda=0.450753
## + Fold08.Rep3: alpha=0.8644, lambda=0.001686
## - Fold08.Rep3: alpha=0.8644, lambda=0.001686
## + Fold08.Rep3: alpha=0.1544, lambda=0.003555
## - Fold08.Rep3: alpha=0.1544, lambda=0.003555
## + Fold09.Rep3: alpha=0.3787, lambda=1.329420
## - Fold09.Rep3: alpha=0.3787, lambda=1.329420
## + Fold09.Rep3: alpha=0.1342, lambda=5.427727
## - Fold09.Rep3: alpha=0.1342, lambda=5.427727
## + Fold09.Rep3: alpha=0.4053, lambda=0.040531
## - Fold09.Rep3: alpha=0.4053, lambda=0.040531
## + Fold09.Rep3: alpha=0.9609, lambda=0.305461
## - Fold09.Rep3: alpha=0.9609, lambda=0.305461
## + Fold09.Rep3: alpha=0.1382, lambda=0.865215
## - Fold09.Rep3: alpha=0.1382, lambda=0.865215
## + Fold09.Rep3: alpha=0.8561, lambda=0.002156
## - Fold09.Rep3: alpha=0.8561, lambda=0.002156
## + Fold09.Rep3: alpha=0.4373, lambda=0.017478
## - Fold09.Rep3: alpha=0.4373, lambda=0.017478
## + Fold09.Rep3: alpha=0.1480, lambda=0.450753
## - Fold09.Rep3: alpha=0.1480, lambda=0.450753
## + Fold09.Rep3: alpha=0.8644, lambda=0.001686
## - Fold09.Rep3: alpha=0.8644, lambda=0.001686
## + Fold09.Rep3: alpha=0.1544, lambda=0.003555
## - Fold09.Rep3: alpha=0.1544, lambda=0.003555
## + Fold10.Rep3: alpha=0.3787, lambda=1.329420
## - Fold10.Rep3: alpha=0.3787, lambda=1.329420
## + Fold10.Rep3: alpha=0.1342, lambda=5.427727
## - Fold10.Rep3: alpha=0.1342, lambda=5.427727
## + Fold10.Rep3: alpha=0.4053, lambda=0.040531
## - Fold10.Rep3: alpha=0.4053, lambda=0.040531
## + Fold10.Rep3: alpha=0.9609, lambda=0.305461
## - Fold10.Rep3: alpha=0.9609, lambda=0.305461
## + Fold10.Rep3: alpha=0.1382, lambda=0.865215
## - Fold10.Rep3: alpha=0.1382, lambda=0.865215
## + Fold10.Rep3: alpha=0.8561, lambda=0.002156
## - Fold10.Rep3: alpha=0.8561, lambda=0.002156
## + Fold10.Rep3: alpha=0.4373, lambda=0.017478
## - Fold10.Rep3: alpha=0.4373, lambda=0.017478
## + Fold10.Rep3: alpha=0.1480, lambda=0.450753
## - Fold10.Rep3: alpha=0.1480, lambda=0.450753
## + Fold10.Rep3: alpha=0.8644, lambda=0.001686
## - Fold10.Rep3: alpha=0.8644, lambda=0.001686
## + Fold10.Rep3: alpha=0.1544, lambda=0.003555
## - Fold10.Rep3: alpha=0.1544, lambda=0.003555
## + Fold01.Rep4: alpha=0.3787, lambda=1.329420
## - Fold01.Rep4: alpha=0.3787, lambda=1.329420
## + Fold01.Rep4: alpha=0.1342, lambda=5.427727
## - Fold01.Rep4: alpha=0.1342, lambda=5.427727
## + Fold01.Rep4: alpha=0.4053, lambda=0.040531
## - Fold01.Rep4: alpha=0.4053, lambda=0.040531
## + Fold01.Rep4: alpha=0.9609, lambda=0.305461
## - Fold01.Rep4: alpha=0.9609, lambda=0.305461
## + Fold01.Rep4: alpha=0.1382, lambda=0.865215
## - Fold01.Rep4: alpha=0.1382, lambda=0.865215
## + Fold01.Rep4: alpha=0.8561, lambda=0.002156
## - Fold01.Rep4: alpha=0.8561, lambda=0.002156
## + Fold01.Rep4: alpha=0.4373, lambda=0.017478
## - Fold01.Rep4: alpha=0.4373, lambda=0.017478
## + Fold01.Rep4: alpha=0.1480, lambda=0.450753
## - Fold01.Rep4: alpha=0.1480, lambda=0.450753
## + Fold01.Rep4: alpha=0.8644, lambda=0.001686
## - Fold01.Rep4: alpha=0.8644, lambda=0.001686
## + Fold01.Rep4: alpha=0.1544, lambda=0.003555
## - Fold01.Rep4: alpha=0.1544, lambda=0.003555
## + Fold02.Rep4: alpha=0.3787, lambda=1.329420
## - Fold02.Rep4: alpha=0.3787, lambda=1.329420
## + Fold02.Rep4: alpha=0.1342, lambda=5.427727
## - Fold02.Rep4: alpha=0.1342, lambda=5.427727
## + Fold02.Rep4: alpha=0.4053, lambda=0.040531
## - Fold02.Rep4: alpha=0.4053, lambda=0.040531
## + Fold02.Rep4: alpha=0.9609, lambda=0.305461
## - Fold02.Rep4: alpha=0.9609, lambda=0.305461
## + Fold02.Rep4: alpha=0.1382, lambda=0.865215
## - Fold02.Rep4: alpha=0.1382, lambda=0.865215
## + Fold02.Rep4: alpha=0.8561, lambda=0.002156
## - Fold02.Rep4: alpha=0.8561, lambda=0.002156
## + Fold02.Rep4: alpha=0.4373, lambda=0.017478
## - Fold02.Rep4: alpha=0.4373, lambda=0.017478
## + Fold02.Rep4: alpha=0.1480, lambda=0.450753
## - Fold02.Rep4: alpha=0.1480, lambda=0.450753
## + Fold02.Rep4: alpha=0.8644, lambda=0.001686
## - Fold02.Rep4: alpha=0.8644, lambda=0.001686
## + Fold02.Rep4: alpha=0.1544, lambda=0.003555
## - Fold02.Rep4: alpha=0.1544, lambda=0.003555
## + Fold03.Rep4: alpha=0.3787, lambda=1.329420
## - Fold03.Rep4: alpha=0.3787, lambda=1.329420
## + Fold03.Rep4: alpha=0.1342, lambda=5.427727
## - Fold03.Rep4: alpha=0.1342, lambda=5.427727
## + Fold03.Rep4: alpha=0.4053, lambda=0.040531
## - Fold03.Rep4: alpha=0.4053, lambda=0.040531
## + Fold03.Rep4: alpha=0.9609, lambda=0.305461
## - Fold03.Rep4: alpha=0.9609, lambda=0.305461
## + Fold03.Rep4: alpha=0.1382, lambda=0.865215
## - Fold03.Rep4: alpha=0.1382, lambda=0.865215
## + Fold03.Rep4: alpha=0.8561, lambda=0.002156
## - Fold03.Rep4: alpha=0.8561, lambda=0.002156
## + Fold03.Rep4: alpha=0.4373, lambda=0.017478
## - Fold03.Rep4: alpha=0.4373, lambda=0.017478
## + Fold03.Rep4: alpha=0.1480, lambda=0.450753
## - Fold03.Rep4: alpha=0.1480, lambda=0.450753
## + Fold03.Rep4: alpha=0.8644, lambda=0.001686
## - Fold03.Rep4: alpha=0.8644, lambda=0.001686
## + Fold03.Rep4: alpha=0.1544, lambda=0.003555
## - Fold03.Rep4: alpha=0.1544, lambda=0.003555
## + Fold04.Rep4: alpha=0.3787, lambda=1.329420
## - Fold04.Rep4: alpha=0.3787, lambda=1.329420
## + Fold04.Rep4: alpha=0.1342, lambda=5.427727
## - Fold04.Rep4: alpha=0.1342, lambda=5.427727
## + Fold04.Rep4: alpha=0.4053, lambda=0.040531
## - Fold04.Rep4: alpha=0.4053, lambda=0.040531
## + Fold04.Rep4: alpha=0.9609, lambda=0.305461
## - Fold04.Rep4: alpha=0.9609, lambda=0.305461
## + Fold04.Rep4: alpha=0.1382, lambda=0.865215
## - Fold04.Rep4: alpha=0.1382, lambda=0.865215
## + Fold04.Rep4: alpha=0.8561, lambda=0.002156
## - Fold04.Rep4: alpha=0.8561, lambda=0.002156
## + Fold04.Rep4: alpha=0.4373, lambda=0.017478
## - Fold04.Rep4: alpha=0.4373, lambda=0.017478
## + Fold04.Rep4: alpha=0.1480, lambda=0.450753
## - Fold04.Rep4: alpha=0.1480, lambda=0.450753
## + Fold04.Rep4: alpha=0.8644, lambda=0.001686
## - Fold04.Rep4: alpha=0.8644, lambda=0.001686
## + Fold04.Rep4: alpha=0.1544, lambda=0.003555
## - Fold04.Rep4: alpha=0.1544, lambda=0.003555
## + Fold05.Rep4: alpha=0.3787, lambda=1.329420
## - Fold05.Rep4: alpha=0.3787, lambda=1.329420
## + Fold05.Rep4: alpha=0.1342, lambda=5.427727
## - Fold05.Rep4: alpha=0.1342, lambda=5.427727
## + Fold05.Rep4: alpha=0.4053, lambda=0.040531
## - Fold05.Rep4: alpha=0.4053, lambda=0.040531
## + Fold05.Rep4: alpha=0.9609, lambda=0.305461
## - Fold05.Rep4: alpha=0.9609, lambda=0.305461
## + Fold05.Rep4: alpha=0.1382, lambda=0.865215
## - Fold05.Rep4: alpha=0.1382, lambda=0.865215
## + Fold05.Rep4: alpha=0.8561, lambda=0.002156
## - Fold05.Rep4: alpha=0.8561, lambda=0.002156
## + Fold05.Rep4: alpha=0.4373, lambda=0.017478
## - Fold05.Rep4: alpha=0.4373, lambda=0.017478
## + Fold05.Rep4: alpha=0.1480, lambda=0.450753
## - Fold05.Rep4: alpha=0.1480, lambda=0.450753
## + Fold05.Rep4: alpha=0.8644, lambda=0.001686
## - Fold05.Rep4: alpha=0.8644, lambda=0.001686
## + Fold05.Rep4: alpha=0.1544, lambda=0.003555
## - Fold05.Rep4: alpha=0.1544, lambda=0.003555
## + Fold06.Rep4: alpha=0.3787, lambda=1.329420
## - Fold06.Rep4: alpha=0.3787, lambda=1.329420
## + Fold06.Rep4: alpha=0.1342, lambda=5.427727
## - Fold06.Rep4: alpha=0.1342, lambda=5.427727
## + Fold06.Rep4: alpha=0.4053, lambda=0.040531
## - Fold06.Rep4: alpha=0.4053, lambda=0.040531
## + Fold06.Rep4: alpha=0.9609, lambda=0.305461
## - Fold06.Rep4: alpha=0.9609, lambda=0.305461
## + Fold06.Rep4: alpha=0.1382, lambda=0.865215
## - Fold06.Rep4: alpha=0.1382, lambda=0.865215
## + Fold06.Rep4: alpha=0.8561, lambda=0.002156
## - Fold06.Rep4: alpha=0.8561, lambda=0.002156
## + Fold06.Rep4: alpha=0.4373, lambda=0.017478
## - Fold06.Rep4: alpha=0.4373, lambda=0.017478
## + Fold06.Rep4: alpha=0.1480, lambda=0.450753
## - Fold06.Rep4: alpha=0.1480, lambda=0.450753
## + Fold06.Rep4: alpha=0.8644, lambda=0.001686
## - Fold06.Rep4: alpha=0.8644, lambda=0.001686
## + Fold06.Rep4: alpha=0.1544, lambda=0.003555
## - Fold06.Rep4: alpha=0.1544, lambda=0.003555
## + Fold07.Rep4: alpha=0.3787, lambda=1.329420
## - Fold07.Rep4: alpha=0.3787, lambda=1.329420
## + Fold07.Rep4: alpha=0.1342, lambda=5.427727
## - Fold07.Rep4: alpha=0.1342, lambda=5.427727
## + Fold07.Rep4: alpha=0.4053, lambda=0.040531
## - Fold07.Rep4: alpha=0.4053, lambda=0.040531
## + Fold07.Rep4: alpha=0.9609, lambda=0.305461
## - Fold07.Rep4: alpha=0.9609, lambda=0.305461
## + Fold07.Rep4: alpha=0.1382, lambda=0.865215
## - Fold07.Rep4: alpha=0.1382, lambda=0.865215
## + Fold07.Rep4: alpha=0.8561, lambda=0.002156
## - Fold07.Rep4: alpha=0.8561, lambda=0.002156
## + Fold07.Rep4: alpha=0.4373, lambda=0.017478
## - Fold07.Rep4: alpha=0.4373, lambda=0.017478
## + Fold07.Rep4: alpha=0.1480, lambda=0.450753
## - Fold07.Rep4: alpha=0.1480, lambda=0.450753
## + Fold07.Rep4: alpha=0.8644, lambda=0.001686
## - Fold07.Rep4: alpha=0.8644, lambda=0.001686
## + Fold07.Rep4: alpha=0.1544, lambda=0.003555
## - Fold07.Rep4: alpha=0.1544, lambda=0.003555
## + Fold08.Rep4: alpha=0.3787, lambda=1.329420
## - Fold08.Rep4: alpha=0.3787, lambda=1.329420
## + Fold08.Rep4: alpha=0.1342, lambda=5.427727
## - Fold08.Rep4: alpha=0.1342, lambda=5.427727
## + Fold08.Rep4: alpha=0.4053, lambda=0.040531
## - Fold08.Rep4: alpha=0.4053, lambda=0.040531
## + Fold08.Rep4: alpha=0.9609, lambda=0.305461
## - Fold08.Rep4: alpha=0.9609, lambda=0.305461
## + Fold08.Rep4: alpha=0.1382, lambda=0.865215
## - Fold08.Rep4: alpha=0.1382, lambda=0.865215
## + Fold08.Rep4: alpha=0.8561, lambda=0.002156
## - Fold08.Rep4: alpha=0.8561, lambda=0.002156
## + Fold08.Rep4: alpha=0.4373, lambda=0.017478
## - Fold08.Rep4: alpha=0.4373, lambda=0.017478
## + Fold08.Rep4: alpha=0.1480, lambda=0.450753
## - Fold08.Rep4: alpha=0.1480, lambda=0.450753
## + Fold08.Rep4: alpha=0.8644, lambda=0.001686
## - Fold08.Rep4: alpha=0.8644, lambda=0.001686
## + Fold08.Rep4: alpha=0.1544, lambda=0.003555
## - Fold08.Rep4: alpha=0.1544, lambda=0.003555
## + Fold09.Rep4: alpha=0.3787, lambda=1.329420
## - Fold09.Rep4: alpha=0.3787, lambda=1.329420
## + Fold09.Rep4: alpha=0.1342, lambda=5.427727
## - Fold09.Rep4: alpha=0.1342, lambda=5.427727
## + Fold09.Rep4: alpha=0.4053, lambda=0.040531
## - Fold09.Rep4: alpha=0.4053, lambda=0.040531
## + Fold09.Rep4: alpha=0.9609, lambda=0.305461
## - Fold09.Rep4: alpha=0.9609, lambda=0.305461
## + Fold09.Rep4: alpha=0.1382, lambda=0.865215
## - Fold09.Rep4: alpha=0.1382, lambda=0.865215
## + Fold09.Rep4: alpha=0.8561, lambda=0.002156
## - Fold09.Rep4: alpha=0.8561, lambda=0.002156
## + Fold09.Rep4: alpha=0.4373, lambda=0.017478
## - Fold09.Rep4: alpha=0.4373, lambda=0.017478
## + Fold09.Rep4: alpha=0.1480, lambda=0.450753
## - Fold09.Rep4: alpha=0.1480, lambda=0.450753
## + Fold09.Rep4: alpha=0.8644, lambda=0.001686
## - Fold09.Rep4: alpha=0.8644, lambda=0.001686
## + Fold09.Rep4: alpha=0.1544, lambda=0.003555
## - Fold09.Rep4: alpha=0.1544, lambda=0.003555
## + Fold10.Rep4: alpha=0.3787, lambda=1.329420
## - Fold10.Rep4: alpha=0.3787, lambda=1.329420
## + Fold10.Rep4: alpha=0.1342, lambda=5.427727
## - Fold10.Rep4: alpha=0.1342, lambda=5.427727
## + Fold10.Rep4: alpha=0.4053, lambda=0.040531
## - Fold10.Rep4: alpha=0.4053, lambda=0.040531
## + Fold10.Rep4: alpha=0.9609, lambda=0.305461
## - Fold10.Rep4: alpha=0.9609, lambda=0.305461
## + Fold10.Rep4: alpha=0.1382, lambda=0.865215
## - Fold10.Rep4: alpha=0.1382, lambda=0.865215
## + Fold10.Rep4: alpha=0.8561, lambda=0.002156
## - Fold10.Rep4: alpha=0.8561, lambda=0.002156
## + Fold10.Rep4: alpha=0.4373, lambda=0.017478
## - Fold10.Rep4: alpha=0.4373, lambda=0.017478
## + Fold10.Rep4: alpha=0.1480, lambda=0.450753
## - Fold10.Rep4: alpha=0.1480, lambda=0.450753
## + Fold10.Rep4: alpha=0.8644, lambda=0.001686
## - Fold10.Rep4: alpha=0.8644, lambda=0.001686
## + Fold10.Rep4: alpha=0.1544, lambda=0.003555
## - Fold10.Rep4: alpha=0.1544, lambda=0.003555
## + Fold01.Rep5: alpha=0.3787, lambda=1.329420
## - Fold01.Rep5: alpha=0.3787, lambda=1.329420
## + Fold01.Rep5: alpha=0.1342, lambda=5.427727
## - Fold01.Rep5: alpha=0.1342, lambda=5.427727
## + Fold01.Rep5: alpha=0.4053, lambda=0.040531
## - Fold01.Rep5: alpha=0.4053, lambda=0.040531
## + Fold01.Rep5: alpha=0.9609, lambda=0.305461
## - Fold01.Rep5: alpha=0.9609, lambda=0.305461
## + Fold01.Rep5: alpha=0.1382, lambda=0.865215
## - Fold01.Rep5: alpha=0.1382, lambda=0.865215
## + Fold01.Rep5: alpha=0.8561, lambda=0.002156
## - Fold01.Rep5: alpha=0.8561, lambda=0.002156
## + Fold01.Rep5: alpha=0.4373, lambda=0.017478
## - Fold01.Rep5: alpha=0.4373, lambda=0.017478
## + Fold01.Rep5: alpha=0.1480, lambda=0.450753
## - Fold01.Rep5: alpha=0.1480, lambda=0.450753
## + Fold01.Rep5: alpha=0.8644, lambda=0.001686
## - Fold01.Rep5: alpha=0.8644, lambda=0.001686
## + Fold01.Rep5: alpha=0.1544, lambda=0.003555
## - Fold01.Rep5: alpha=0.1544, lambda=0.003555
## + Fold02.Rep5: alpha=0.3787, lambda=1.329420
## - Fold02.Rep5: alpha=0.3787, lambda=1.329420
## + Fold02.Rep5: alpha=0.1342, lambda=5.427727
## - Fold02.Rep5: alpha=0.1342, lambda=5.427727
## + Fold02.Rep5: alpha=0.4053, lambda=0.040531
## - Fold02.Rep5: alpha=0.4053, lambda=0.040531
## + Fold02.Rep5: alpha=0.9609, lambda=0.305461
## - Fold02.Rep5: alpha=0.9609, lambda=0.305461
## + Fold02.Rep5: alpha=0.1382, lambda=0.865215
## - Fold02.Rep5: alpha=0.1382, lambda=0.865215
## + Fold02.Rep5: alpha=0.8561, lambda=0.002156
## - Fold02.Rep5: alpha=0.8561, lambda=0.002156
## + Fold02.Rep5: alpha=0.4373, lambda=0.017478
## - Fold02.Rep5: alpha=0.4373, lambda=0.017478
## + Fold02.Rep5: alpha=0.1480, lambda=0.450753
## - Fold02.Rep5: alpha=0.1480, lambda=0.450753
## + Fold02.Rep5: alpha=0.8644, lambda=0.001686
## - Fold02.Rep5: alpha=0.8644, lambda=0.001686
## + Fold02.Rep5: alpha=0.1544, lambda=0.003555
## - Fold02.Rep5: alpha=0.1544, lambda=0.003555
## + Fold03.Rep5: alpha=0.3787, lambda=1.329420
## - Fold03.Rep5: alpha=0.3787, lambda=1.329420
## + Fold03.Rep5: alpha=0.1342, lambda=5.427727
## - Fold03.Rep5: alpha=0.1342, lambda=5.427727
## + Fold03.Rep5: alpha=0.4053, lambda=0.040531
## - Fold03.Rep5: alpha=0.4053, lambda=0.040531
## + Fold03.Rep5: alpha=0.9609, lambda=0.305461
## - Fold03.Rep5: alpha=0.9609, lambda=0.305461
## + Fold03.Rep5: alpha=0.1382, lambda=0.865215
## - Fold03.Rep5: alpha=0.1382, lambda=0.865215
## + Fold03.Rep5: alpha=0.8561, lambda=0.002156
## - Fold03.Rep5: alpha=0.8561, lambda=0.002156
## + Fold03.Rep5: alpha=0.4373, lambda=0.017478
## - Fold03.Rep5: alpha=0.4373, lambda=0.017478
## + Fold03.Rep5: alpha=0.1480, lambda=0.450753
## - Fold03.Rep5: alpha=0.1480, lambda=0.450753
## + Fold03.Rep5: alpha=0.8644, lambda=0.001686
## - Fold03.Rep5: alpha=0.8644, lambda=0.001686
## + Fold03.Rep5: alpha=0.1544, lambda=0.003555
## - Fold03.Rep5: alpha=0.1544, lambda=0.003555
## + Fold04.Rep5: alpha=0.3787, lambda=1.329420
## - Fold04.Rep5: alpha=0.3787, lambda=1.329420
## + Fold04.Rep5: alpha=0.1342, lambda=5.427727
## - Fold04.Rep5: alpha=0.1342, lambda=5.427727
## + Fold04.Rep5: alpha=0.4053, lambda=0.040531
## - Fold04.Rep5: alpha=0.4053, lambda=0.040531
## + Fold04.Rep5: alpha=0.9609, lambda=0.305461
## - Fold04.Rep5: alpha=0.9609, lambda=0.305461
## + Fold04.Rep5: alpha=0.1382, lambda=0.865215
## - Fold04.Rep5: alpha=0.1382, lambda=0.865215
## + Fold04.Rep5: alpha=0.8561, lambda=0.002156
## - Fold04.Rep5: alpha=0.8561, lambda=0.002156
## + Fold04.Rep5: alpha=0.4373, lambda=0.017478
## - Fold04.Rep5: alpha=0.4373, lambda=0.017478
## + Fold04.Rep5: alpha=0.1480, lambda=0.450753
## - Fold04.Rep5: alpha=0.1480, lambda=0.450753
## + Fold04.Rep5: alpha=0.8644, lambda=0.001686
## - Fold04.Rep5: alpha=0.8644, lambda=0.001686
## + Fold04.Rep5: alpha=0.1544, lambda=0.003555
## - Fold04.Rep5: alpha=0.1544, lambda=0.003555
## + Fold05.Rep5: alpha=0.3787, lambda=1.329420
## - Fold05.Rep5: alpha=0.3787, lambda=1.329420
## + Fold05.Rep5: alpha=0.1342, lambda=5.427727
## - Fold05.Rep5: alpha=0.1342, lambda=5.427727
## + Fold05.Rep5: alpha=0.4053, lambda=0.040531
## - Fold05.Rep5: alpha=0.4053, lambda=0.040531
## + Fold05.Rep5: alpha=0.9609, lambda=0.305461
## - Fold05.Rep5: alpha=0.9609, lambda=0.305461
## + Fold05.Rep5: alpha=0.1382, lambda=0.865215
## - Fold05.Rep5: alpha=0.1382, lambda=0.865215
## + Fold05.Rep5: alpha=0.8561, lambda=0.002156
## - Fold05.Rep5: alpha=0.8561, lambda=0.002156
## + Fold05.Rep5: alpha=0.4373, lambda=0.017478
## - Fold05.Rep5: alpha=0.4373, lambda=0.017478
## + Fold05.Rep5: alpha=0.1480, lambda=0.450753
## - Fold05.Rep5: alpha=0.1480, lambda=0.450753
## + Fold05.Rep5: alpha=0.8644, lambda=0.001686
## - Fold05.Rep5: alpha=0.8644, lambda=0.001686
## + Fold05.Rep5: alpha=0.1544, lambda=0.003555
## - Fold05.Rep5: alpha=0.1544, lambda=0.003555
## + Fold06.Rep5: alpha=0.3787, lambda=1.329420
## - Fold06.Rep5: alpha=0.3787, lambda=1.329420
## + Fold06.Rep5: alpha=0.1342, lambda=5.427727
## - Fold06.Rep5: alpha=0.1342, lambda=5.427727
## + Fold06.Rep5: alpha=0.4053, lambda=0.040531
## - Fold06.Rep5: alpha=0.4053, lambda=0.040531
## + Fold06.Rep5: alpha=0.9609, lambda=0.305461
## - Fold06.Rep5: alpha=0.9609, lambda=0.305461
## + Fold06.Rep5: alpha=0.1382, lambda=0.865215
## - Fold06.Rep5: alpha=0.1382, lambda=0.865215
## + Fold06.Rep5: alpha=0.8561, lambda=0.002156
## - Fold06.Rep5: alpha=0.8561, lambda=0.002156
## + Fold06.Rep5: alpha=0.4373, lambda=0.017478
## - Fold06.Rep5: alpha=0.4373, lambda=0.017478
## + Fold06.Rep5: alpha=0.1480, lambda=0.450753
## - Fold06.Rep5: alpha=0.1480, lambda=0.450753
## + Fold06.Rep5: alpha=0.8644, lambda=0.001686
## - Fold06.Rep5: alpha=0.8644, lambda=0.001686
## + Fold06.Rep5: alpha=0.1544, lambda=0.003555
## - Fold06.Rep5: alpha=0.1544, lambda=0.003555
## + Fold07.Rep5: alpha=0.3787, lambda=1.329420
## - Fold07.Rep5: alpha=0.3787, lambda=1.329420
## + Fold07.Rep5: alpha=0.1342, lambda=5.427727
## - Fold07.Rep5: alpha=0.1342, lambda=5.427727
## + Fold07.Rep5: alpha=0.4053, lambda=0.040531
## - Fold07.Rep5: alpha=0.4053, lambda=0.040531
## + Fold07.Rep5: alpha=0.9609, lambda=0.305461
## - Fold07.Rep5: alpha=0.9609, lambda=0.305461
## + Fold07.Rep5: alpha=0.1382, lambda=0.865215
## - Fold07.Rep5: alpha=0.1382, lambda=0.865215
## + Fold07.Rep5: alpha=0.8561, lambda=0.002156
## - Fold07.Rep5: alpha=0.8561, lambda=0.002156
## + Fold07.Rep5: alpha=0.4373, lambda=0.017478
## - Fold07.Rep5: alpha=0.4373, lambda=0.017478
## + Fold07.Rep5: alpha=0.1480, lambda=0.450753
## - Fold07.Rep5: alpha=0.1480, lambda=0.450753
## + Fold07.Rep5: alpha=0.8644, lambda=0.001686
## - Fold07.Rep5: alpha=0.8644, lambda=0.001686
## + Fold07.Rep5: alpha=0.1544, lambda=0.003555
## - Fold07.Rep5: alpha=0.1544, lambda=0.003555
## + Fold08.Rep5: alpha=0.3787, lambda=1.329420
## - Fold08.Rep5: alpha=0.3787, lambda=1.329420
## + Fold08.Rep5: alpha=0.1342, lambda=5.427727
## - Fold08.Rep5: alpha=0.1342, lambda=5.427727
## + Fold08.Rep5: alpha=0.4053, lambda=0.040531
## - Fold08.Rep5: alpha=0.4053, lambda=0.040531
## + Fold08.Rep5: alpha=0.9609, lambda=0.305461
## - Fold08.Rep5: alpha=0.9609, lambda=0.305461
## + Fold08.Rep5: alpha=0.1382, lambda=0.865215
## - Fold08.Rep5: alpha=0.1382, lambda=0.865215
## + Fold08.Rep5: alpha=0.8561, lambda=0.002156
## - Fold08.Rep5: alpha=0.8561, lambda=0.002156
## + Fold08.Rep5: alpha=0.4373, lambda=0.017478
## - Fold08.Rep5: alpha=0.4373, lambda=0.017478
## + Fold08.Rep5: alpha=0.1480, lambda=0.450753
## - Fold08.Rep5: alpha=0.1480, lambda=0.450753
## + Fold08.Rep5: alpha=0.8644, lambda=0.001686
## - Fold08.Rep5: alpha=0.8644, lambda=0.001686
## + Fold08.Rep5: alpha=0.1544, lambda=0.003555
## - Fold08.Rep5: alpha=0.1544, lambda=0.003555
## + Fold09.Rep5: alpha=0.3787, lambda=1.329420
## - Fold09.Rep5: alpha=0.3787, lambda=1.329420
## + Fold09.Rep5: alpha=0.1342, lambda=5.427727
## - Fold09.Rep5: alpha=0.1342, lambda=5.427727
## + Fold09.Rep5: alpha=0.4053, lambda=0.040531
## - Fold09.Rep5: alpha=0.4053, lambda=0.040531
## + Fold09.Rep5: alpha=0.9609, lambda=0.305461
## - Fold09.Rep5: alpha=0.9609, lambda=0.305461
## + Fold09.Rep5: alpha=0.1382, lambda=0.865215
## - Fold09.Rep5: alpha=0.1382, lambda=0.865215
## + Fold09.Rep5: alpha=0.8561, lambda=0.002156
## - Fold09.Rep5: alpha=0.8561, lambda=0.002156
## + Fold09.Rep5: alpha=0.4373, lambda=0.017478
## - Fold09.Rep5: alpha=0.4373, lambda=0.017478
## + Fold09.Rep5: alpha=0.1480, lambda=0.450753
## - Fold09.Rep5: alpha=0.1480, lambda=0.450753
## + Fold09.Rep5: alpha=0.8644, lambda=0.001686
## - Fold09.Rep5: alpha=0.8644, lambda=0.001686
## + Fold09.Rep5: alpha=0.1544, lambda=0.003555
## - Fold09.Rep5: alpha=0.1544, lambda=0.003555
## + Fold10.Rep5: alpha=0.3787, lambda=1.329420
## - Fold10.Rep5: alpha=0.3787, lambda=1.329420
## + Fold10.Rep5: alpha=0.1342, lambda=5.427727
## - Fold10.Rep5: alpha=0.1342, lambda=5.427727
## + Fold10.Rep5: alpha=0.4053, lambda=0.040531
## - Fold10.Rep5: alpha=0.4053, lambda=0.040531
## + Fold10.Rep5: alpha=0.9609, lambda=0.305461
## - Fold10.Rep5: alpha=0.9609, lambda=0.305461
## + Fold10.Rep5: alpha=0.1382, lambda=0.865215
## - Fold10.Rep5: alpha=0.1382, lambda=0.865215
## + Fold10.Rep5: alpha=0.8561, lambda=0.002156
## - Fold10.Rep5: alpha=0.8561, lambda=0.002156
## + Fold10.Rep5: alpha=0.4373, lambda=0.017478
## - Fold10.Rep5: alpha=0.4373, lambda=0.017478
## + Fold10.Rep5: alpha=0.1480, lambda=0.450753
## - Fold10.Rep5: alpha=0.1480, lambda=0.450753
## + Fold10.Rep5: alpha=0.8644, lambda=0.001686
## - Fold10.Rep5: alpha=0.8644, lambda=0.001686
## + Fold10.Rep5: alpha=0.1544, lambda=0.003555
## - Fold10.Rep5: alpha=0.1544, lambda=0.003555
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.154, lambda = 0.00355 on full training set
# Best tuning parameter
elastic_reg$bestTune
## alpha lambda
## 4 0.1543657 0.003554825
# Make predictions on training set
predictions_train <- predict(elastic_reg, x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.605046 0.3789535
# Make predictions on test set
predictions_test <- predict(elastic_reg, x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.7385578 0.3150998
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
ggplot(data = df, mapping = aes(x = total.sulfur.dioxide, y = quality)) +
geom_point()
ggplot(data = df, mapping = aes(x = residual.sugar, y = quality)) +
geom_point()
There is really no relationship. This is probably an exercise in clusterting or machine learning, but linear regression is insufficient.
ggplot(data = df, mapping = aes(x = alcohol, y = quality)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'